Problem: Solve for $x$ and $y$ using elimination. ${3x-4y = -3}$ ${-x+3y = 11}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${3x-4y = -3}$ $-3x+9y = 33$ Add the top and bottom equations together. $5y = 30$ $\dfrac{5y}{{5}} = \dfrac{30}{{5}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {3x-4y = -3}\thinspace$ to find $x$ ${3x - 4}{(6)}{= -3}$ $3x-24 = -3$ $3x-24{+24} = -3{+24}$ $3x = 21$ $\dfrac{3x}{{3}} = \dfrac{21}{{3}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {-x+3y = 11}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(6)}{= 11}$ ${x = 7}$